Find the requested confidence interval.
-A college statistics professor has office hours from 9:00 A.M. to 10:30 A.M. daily. A sample of waiting times to see the professor (in minutes) is 10, 12, 20, 15, 17, 10, 30, 28, 35, 28, 19, 27, 25, 22, 33, $37,14,21,20$, 23. Assuming $\sigma = 7.84$, find the $95.44 \%$ confidence interval for the population mean.
A)$18.8$ to $25.8$ minutes
B) $- 3.5$ to $3.5$ minutes
C) $- 7.7$ to $7.8$ minutes
D) $19.5$ to $35.1$ minutes

Question

Find the requested confidence interval.
-A college statistics professor has office hours from 9:00 A.M. to 10:30 A.M. daily. A sample of waiting times to see the professor (in minutes) is 10, 12, 20, 15, 17, 10, 30, 28, 35, 28, 19, 27, 25, 22, 33, $37,14,21,20$, 23. Assuming $\sigma = 7.84$, find the $95.44 \%$ confidence interval for the population mean.  
A)$18.8$ to $25.8$ minutes
B) $- 3.5$ to $3.5$ minutes
C) $- 7.7$ to $7.8$ minutes
D) $19.5$ to $35.1$ minutes

Quizplus · Accepted Answer

Given the sample size (n = 20), the sample mean ($\bar{x}$), and the population standard deviation ($\sigma = 7.84$), we can calculate the 95.44% confidence interval for the population mean using the formula for the confidence interval when the population standard deviation is known, which is $\bar{x} \pm Z \frac{\sigma}{\sqrt{n}}$. The Z-value for a 95.44% confidence level is approximately 2 (more precisely, 2.05 for a two-tailed test from the Z-table, but 2 is a common approximation used for quick calculations). The sample mean ($\bar{x}$) can be calculated from the provided data. Calculating the mean of the provided data gives us a mean ($\bar{x}$) of approximately 22.3 minutes. Using the formula with a Z-value of 2, the margin of error (ME) is $2 \times \frac{7.84}{\sqrt{20}}$, which calculates to approximately 3.5. Therefore, the confidence interval is $22.3 \pm 3.5$, which gives us an interval from approximately 18.8 to 25.8 minutes, matching option A.

Find the Requested Confidence Interval 37,14,21,2037,14,21,2037,14,21,20 , 23 Assuming σ=7.84\sigma = 7.84σ=7.84

Find the Requested Confidence Interval $37,14,21,20$ , 23 Assuming $\sigma = 7.84$